MinT - Best Known (177−50, 177, s)-Nets in Base 2

Best Known (177−50, 177, s)-Nets in Base 2

(177−50, 177, 135)-Net over F₂ — Constructive and digital

Digital (127, 177, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 59, 45)-net over F₈, using
- net from sequence [i] based on digital (9, 44)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]

(177−50, 177, 186)-Net over F₂ — Digital

Digital (127, 177, 186)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−50, 177, 1340)-Net in Base 2 — Upper bound on s

There is no (127, 177, 1341)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 193668 737995 726912 754937 715556 135147 028380 599064 660870 > 2¹⁷⁷ [i]